<p>Motivated by research problems arising in the analysis of economic and geochemical data, we consider sufficient dimension reduction in regression with multiple compositional predictors. We develop a second-moment-based method that respects the unique features of compositional data. The proposed method is model-free and can fully recover the central dimension-reduction subspace, which then allows us to derive a sufficient reduction of the compositional predictors. In addition, we suggest a Bayesian-type information criterion to determine the structural dimension of the central subspace. Extensive simulation studies and an application to a disposable income of Chinese urban residents data set demonstrate the effectiveness and efficiency of the method.</p>